Trend simulation
Mladen Jovanovic
9/15/2020
Simulation #1
True score 1RM stays the same across two measures, but observed score varies due to biological variation and predicted (or practical in this case) also varies due to the measurement error.
require(tidyverse)
require(bmbstats)
require(DT)
require(cowplot)
biological_fixed <- 0
biological_proportional <- 1
biological_random <- 3
measurement_fixed <- 0
measurement_proportional <- 1
measurement_random <- 3
n_athletes <- 50
SESOI <- 5
random.seed <- 1667
boot_samples <- 2000
confidence <- 0.95
boot_type <- "bca"
# ==========================================
set.seed(random.seed)
data_1RM <- tibble(
Athlete = paste0("Athlete", seq(1, n_athletes)),
TS1 = rnorm(n_athletes, 100, 10),
TS2 = TS1 + rnorm(n_athletes, 0, 0),
TSdiff = TS2 - TS1,
OS1 = biological_fixed + biological_proportional * TS1 + rnorm(n_athletes, 0, biological_random),
OS2 = biological_fixed + biological_proportional * TS2 + rnorm(n_athletes, 0, biological_random),
OSdiff = OS2 - OS1,
PS1 = measurement_fixed + measurement_proportional * OS1 + rnorm(n_athletes, 0, measurement_random),
PS2 = measurement_fixed + measurement_proportional * OS2 + rnorm(n_athletes, 0, measurement_random),
PSdiff = PS2 - PS1
)
datatable(data_1RM, rownames = FALSE, filter = "top") %>%
formatRound(columns = 2:ncol(data_1RM), digits = 2)Analysis and plotting functions
my_estimators <- function(data,
trial1,
trial2,
SESOI_lower = 0,
SESOI_upper = 0,
na.rm = FALSE) {
predicted <- data[[trial1]]
observed <- data[[trial2]]
SESOI_range <- SESOI_upper - SESOI_lower
mean_diff <- mean(predicted - observed, na.rm = na.rm)
# perc_diff <- 100 * mean((predicted - observed) / observed, na.rm = na.rm)
sd_diff <- sd(predicted - observed, na.rm = na.rm)
model <- lm(observed ~ predicted)
rse <- summary(model)$sigma
pper <- PPER(
sigma = rse,
SESOI_lower = SESOI_lower,
SESOI_upper = SESOI_upper,
df = length(observed) - 2
)
sdc <- rse * stats::qt(1 - ((1 - 0.95) / 2), df = length(observed) - 2)
# TE <- rse / sqrt(2)
# cv <- 100 * TE / mean(observed)
MAD <- mean(abs(predicted - observed), na.rm = na.rm)
# MAPD <- 100 * mean(abs((predicted - observed) / observed), na.rm = na.rm)
c(
# `SESOI lower` = SESOI_lower,
# `SESOI_upper` = SESOI_upper,
`Mean Diff` = mean_diff,
# `% Diff` = perc_diff,
`SD Diff` = sd_diff,
MAD = MAD,
# Intercept = coef(model)[[1]],
# Slope = coef(model)[[2]],
RSE = rse,
PPER = pper,
# TE = TE,
SDC = sdc
# `%CV` = cv,
# MAPD = MAPD
)
}
# ===========================
analyse_func <- function(data, predictor, outcome) {
data <- data.frame(
predictor = data[[predictor]],
outcome = data[[outcome]]
)
estimators <- my_estimators(
data = na.omit(data),
trial1 = "predictor",
trial2 = "outcome",
SESOI_lower = -SESOI,
SESOI_upper = SESOI
)
estimators_text <- paste0(names(estimators), "=", round(estimators, 2), collapse = ", ")
# Bland Altman
gg <- plot_grid(
ggdraw() + draw_label(estimators_text,
fontface='italic', size = 10),
plot_grid(
plot_pair_changes(
group_a = data$predictor,
group_b = data$outcome,
group_a_label = predictor,
group_b_label = outcome,
SESOI_lower = -SESOI,
SESOI_upper = SESOI),
plot_pair_lm(
predictor = data$predictor,
outcome = data$outcome,
predictor_label = predictor,
outcome_label = outcome,
SESOI_lower = -SESOI,
SESOI_upper = SESOI,
na.rm = TRUE,
control = plot_control(panel_labels = c(NULL, NULL))),
nrow = 1,
rel_widths = c(1, 2)),
ncol = 1,
rel_heights = c(0.1, 1))
print(gg)
boot_estimators <- reliability_analysis(
data,
trial1 = "predictor",
trial2 = "outcome",
SESOI_lower = function(...) -SESOI,
SESOI_upper = function(...) SESOI,
estimator_function = my_estimators,
control = model_control(
boot_type = boot_type,
boot_samples = boot_samples,
seed = random.seed,
iter = FALSE
),
na.rm = TRUE
)
print(boot_estimators)
return(boot_estimators)
}Plotting and analysis
Repeatability
TS1_TS2 <- analyse_func(data_1RM, "TS1", "TS2")
#> [1] "All values of t are equal to 1 \n Cannot calculate confidence intervals"
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff 0.000000e+00 NA NA
#> SD Diff 0.000000e+00 NA NA
#> MAD 0.000000e+00 NA NA
#> RSE 3.204942e-16 0 4.562373e-16
#> PPER 1.000000e+00 NA NA
#> SDC 6.443967e-16 0 9.173266e-16
OS1_OS2 <- analyse_func(data_1RM, "OS1", "OS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff 0.1989543 -0.9518448 1.2243814
#> SD Diff 3.9189576 3.3863430 5.0397272
#> MAD 3.2865627 2.7698220 3.9811601
#> RSE 3.6309941 3.2069235 4.4229834
#> PPER 0.8251096 0.7361123 0.8744657
#> SDC 7.3006029 6.4479519 8.8930041
PS1_PS2 <- analyse_func(data_1RM, "PS1", "PS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -0.1440930 -2.1090574 1.5880397
#> SD Diff 6.7266837 5.7008578 8.1745999
#> MAD 5.4175211 4.4707010 6.6616170
#> RSE 5.7337687 4.9491072 6.9338084
#> PPER 0.6124651 0.5256624 0.6825777
#> SDC 11.5285146 9.9508470 13.9413562
Validity (Prediction)
Observed vs True
OS1_TS1 <- analyse_func(data_1RM, "OS1", "TS1")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -0.6486222 -1.412789 0.07847829
#> SD Diff 2.7669426 2.368255 3.33230593
#> MAD 2.2802496 1.822822 2.77875002
#> RSE 2.5832908 2.216105 3.13354241
#> PPER 0.9411704 0.882704 0.97134208
#> SDC 5.1940542 4.455777 6.30040928
OS2_TS2 <- analyse_func(data_1RM, "OS2", "TS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -0.8475765 -1.5309040 -0.1400448
#> SD Diff 2.5523202 2.2026842 3.0327781
#> MAD 2.1829967 1.7815176 2.6322982
#> RSE 2.5678697 2.2188811 3.1095988
#> PPER 0.9426184 0.8854911 0.9711095
#> SDC 5.1630480 4.4613595 6.2522674
OSdiff_TSdiff <- analyse_func(data_1RM, "OSdiff", "TSdiff")
#> [1] "All values of t are equal to 1 \n Cannot calculate confidence intervals"
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -0.1989543 -1.224381 0.9518448
#> SD Diff 3.9189576 3.386343 5.0397272
#> MAD 3.2865627 2.769822 3.9811601
#> RSE 0.0000000 NA NA
#> PPER 1.0000000 NA NA
#> SDC 0.0000000 NA NA
Predicted vs True
PS1_TS1 <- analyse_func(data_1RM, "PS1", "TS1")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -0.8103587 -2.0602135 0.4857175
#> SD Diff 4.6875924 4.0168326 5.6232430
#> MAD 3.7346413 3.0057163 4.6084908
#> RSE 3.8726629 3.3879259 4.6394978
#> PPER 0.7971479 0.7134523 0.8534933
#> SDC 7.7865107 6.8118816 9.3283355
PS2_TS2 <- analyse_func(data_1RM, "PS2", "TS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -0.6662657 -1.8312715 0.4321591
#> SD Diff 4.2112919 3.6186068 5.0396329
#> MAD 3.5473282 2.9625700 4.2314086
#> RSE 4.1026745 3.5310305 4.9374405
#> PPER 0.7710925 0.6837198 0.8367766
#> SDC 8.2489800 7.0996126 9.9273895
PSdiff_TSdiff <- analyse_func(data_1RM, "PSdiff", "TSdiff")
#> [1] "All values of t are equal to 1 \n Cannot calculate confidence intervals"
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff 0.144093 -1.588040 2.109057
#> SD Diff 6.726684 5.700858 8.174600
#> MAD 5.417521 4.470701 6.661617
#> RSE 0.000000 NA NA
#> PPER 1.000000 NA NA
#> SDC 0.000000 NA NA
Predicted vs Observed
PS1_OS1 <- analyse_func(data_1RM, "PS1", "OS1")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -0.1617365 -1.0211939 0.8056034
#> SD Diff 3.3630665 2.7931604 4.2245840
#> MAD 2.6118866 2.1240580 3.2592150
#> RSE 2.9798010 2.5403930 3.7393982
#> PPER 0.9001455 0.8124409 0.9451003
#> SDC 5.9912915 5.1078025 7.5185640
PS2_OS2 <- analyse_func(data_1RM, "PS2", "OS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff 0.1813108 -0.6796237 1.0308761
#> SD Diff 3.0902968 2.5383326 3.9167088
#> MAD 2.3630119 1.9015453 2.9935957
#> RSE 3.0158782 2.5267683 3.6938464
#> PPER 0.8961385 0.8177925 0.9463232
#> SDC 6.0638295 5.0804082 7.4269759
PSdiff_OSdiff <- analyse_func(data_1RM, "PSdiff", "OSdiff")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff 0.3430474 -1.1634691 1.7208791
#> SD Diff 5.2144206 4.4086620 6.2622832
#> MAD 4.1600530 3.3683048 5.0470001
#> RSE 3.0626923 2.4719221 3.9172739
#> PPER 0.8908925 0.7920281 0.9512094
#> SDC 6.1579557 4.9701326 7.8762071
Save estimators in data frame:
experiment1 <- rbind(
data.frame(experiment = "1", comparison = "TS1 vs. TS2", TS1_TS2$estimators),
data.frame(experiment = "1", comparison = "OS1 vs. OS2", OS1_OS2$estimators),
data.frame(experiment = "1", comparison = "PS1 vs. PS2", PS1_PS2$estimators),
data.frame(experiment = "1", comparison = "OS1 vs. TS1", OS1_TS1$estimators),
data.frame(experiment = "1", comparison = "OS2 vs. TS2", OS2_TS2$estimators),
data.frame(experiment = "1", comparison = "OSdiff vs. TSdiff", OSdiff_TSdiff$estimators),
data.frame(experiment = "1", comparison = "PS1 vs. TS1", PS1_TS1$estimators),
data.frame(experiment = "1", comparison = "PS2 vs. TS2", PS2_TS2$estimators),
data.frame(experiment = "1", comparison = "PSdiff vs. TSdiff", PSdiff_TSdiff$estimators),
data.frame(experiment = "1", comparison = "PS1 vs. OS1", PS1_OS1$estimators),
data.frame(experiment = "1", comparison = "PS2 vs. OS2", PS2_OS2$estimators),
data.frame(experiment = "1", comparison = "PSdiff vs. OSdiff", PSdiff_OSdiff$estimators)
)
experiment1 <- experiment1 %>%
mutate(
comparison = factor(comparison),
estimator = factor(estimator))
datatable(experiment1, rownames = FALSE, filter = "top") %>%
formatRound(columns = 4:ncol(experiment1), digits = 2)Simulation #2
In this simulation there is true change in 1RM, where everyone improves for 10kg. Let’s see how that plays out
set.seed(random.seed)
data_1RM <- tibble(
Athlete = paste0("Athlete", seq(1, n_athletes)),
TS1 = rnorm(n_athletes, 100, 10),
TS2 = TS1 + rnorm(n_athletes, 10, 0),
TSdiff = TS2 - TS1,
OS1 = biological_fixed + biological_proportional * TS1 + rnorm(n_athletes, 0, biological_random),
OS2 = biological_fixed + biological_proportional * TS2 + rnorm(n_athletes, 0, biological_random),
OSdiff = OS2 - OS1,
PS1 = measurement_fixed + measurement_proportional * OS1 + rnorm(n_athletes, 0, measurement_random),
PS2 = measurement_fixed + measurement_proportional * OS2 + rnorm(n_athletes, 0, measurement_random),
PSdiff = PS2 - PS1
)
datatable(data_1RM, rownames = FALSE, filter = "top") %>%
formatRound(columns = 2:ncol(data_1RM), digits = 2)Plotting and analysis
Repeatability
TS1_TS2 <- analyse_func(data_1RM, "TS1", "TS2")
#> [1] "All values of t are equal to 10 \n Cannot calculate confidence intervals"
#> [1] "All values of t are equal to 1 \n Cannot calculate confidence intervals"
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -1.000000e+01 NA NA
#> SD Diff 0.000000e+00 NA NA
#> MAD 1.000000e+01 NA NA
#> RSE 3.204942e-16 0 2.099946e-16
#> PPER 1.000000e+00 NA NA
#> SDC 6.443967e-16 0 4.222225e-16
OS1_OS2 <- analyse_func(data_1RM, "OS1", "OS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -9.8010457 -10.9518448 -8.7756186
#> SD Diff 3.9189576 3.3863430 5.0397272
#> MAD 9.8010457 8.7756186 10.9518448
#> RSE 3.6309941 3.2069235 4.4229834
#> PPER 0.8251096 0.7361123 0.8744657
#> SDC 7.3006029 6.4479519 8.8930041
PS1_PS2 <- analyse_func(data_1RM, "PS1", "PS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -10.1440930 -12.1090574 -8.4119603
#> SD Diff 6.7266837 5.7008578 8.1745999
#> MAD 10.3115951 8.6279317 12.2735568
#> RSE 5.7337687 4.9491072 6.9338084
#> PPER 0.6124651 0.5256624 0.6825777
#> SDC 11.5285146 9.9508470 13.9413562
Validity (Prediction)
Observed vs True
OS1_TS1 <- analyse_func(data_1RM, "OS1", "TS1")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -0.6486222 -1.412789 0.07847829
#> SD Diff 2.7669426 2.368255 3.33230593
#> MAD 2.2802496 1.822822 2.77875002
#> RSE 2.5832908 2.216105 3.13354241
#> PPER 0.9411704 0.882704 0.97134208
#> SDC 5.1940542 4.455777 6.30040928
OS2_TS2 <- analyse_func(data_1RM, "OS2", "TS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -0.8475765 -1.5309040 -0.1400448
#> SD Diff 2.5523202 2.2026842 3.0327781
#> MAD 2.1829967 1.7815176 2.6322982
#> RSE 2.5678697 2.2188811 3.1095988
#> PPER 0.9426184 0.8854911 0.9711095
#> SDC 5.1630480 4.4613595 6.2522674
OSdiff_TSdiff <- analyse_func(data_1RM, "OSdiff", "TSdiff")
#> [1] "All values of t are equal to 1 \n Cannot calculate confidence intervals"
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -1.989543e-01 -1.224381e+00 9.518448e-01
#> SD Diff 3.918958e+00 3.386343e+00 5.039727e+00
#> MAD 3.286563e+00 2.769822e+00 3.981160e+00
#> RSE 1.061678e-14 9.701006e-15 1.073966e-14
#> PPER 1.000000e+00 NA NA
#> SDC 2.134648e-14 1.950518e-14 2.159353e-14
Predicted vs True
PS1_TS1 <- analyse_func(data_1RM, "PS1", "TS1")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -0.8103587 -2.0602135 0.4857175
#> SD Diff 4.6875924 4.0168326 5.6232430
#> MAD 3.7346413 3.0057163 4.6084908
#> RSE 3.8726629 3.3879259 4.6394978
#> PPER 0.7971479 0.7134523 0.8534933
#> SDC 7.7865107 6.8118816 9.3283355
PS2_TS2 <- analyse_func(data_1RM, "PS2", "TS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -0.6662657 -1.8312715 0.4321591
#> SD Diff 4.2112919 3.6186068 5.0396329
#> MAD 3.5473282 2.9625700 4.2314086
#> RSE 4.1026745 3.5310305 4.9374405
#> PPER 0.7710925 0.6837198 0.8367766
#> SDC 8.2489800 7.0996126 9.9273895
PSdiff_TSdiff <- analyse_func(data_1RM, "PSdiff", "TSdiff")
#> [1] "All values of t are equal to 1 \n Cannot calculate confidence intervals"
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff 1.440930e-01 -1.588040e+00 2.109057e+00
#> SD Diff 6.726684e+00 5.700858e+00 8.174600e+00
#> MAD 5.417521e+00 4.470701e+00 6.661617e+00
#> RSE 1.073058e-14 1.030554e-14 1.076850e-14
#> PPER 1.000000e+00 NA NA
#> SDC 2.157529e-14 2.072067e-14 2.165152e-14
Predicted vs Observed
PS1_OS1 <- analyse_func(data_1RM, "PS1", "OS1")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -0.1617365 -1.0211939 0.8056034
#> SD Diff 3.3630665 2.7931604 4.2245840
#> MAD 2.6118866 2.1240580 3.2592150
#> RSE 2.9798010 2.5403930 3.7393982
#> PPER 0.9001455 0.8124409 0.9451003
#> SDC 5.9912915 5.1078025 7.5185640
PS2_OS2 <- analyse_func(data_1RM, "PS2", "OS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff 0.1813108 -0.6796237 1.0308761
#> SD Diff 3.0902968 2.5383326 3.9167088
#> MAD 2.3630119 1.9015453 2.9935957
#> RSE 3.0158782 2.5267683 3.6938464
#> PPER 0.8961385 0.8177925 0.9463232
#> SDC 6.0638295 5.0804082 7.4269759
PSdiff_OSdiff <- analyse_func(data_1RM, "PSdiff", "OSdiff")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff 0.3430474 -1.1634691 1.7208791
#> SD Diff 5.2144206 4.4086620 6.2622832
#> MAD 4.1600530 3.3683048 5.0470001
#> RSE 3.0626923 2.4719221 3.9172739
#> PPER 0.8908925 0.7920281 0.9512094
#> SDC 6.1579557 4.9701326 7.8762071
Save estimators in data frame:
experiment2 <- rbind(
data.frame(experiment = "2", comparison = "TS1 vs. TS2", TS1_TS2$estimators),
data.frame(experiment = "2", comparison = "OS1 vs. OS2", OS1_OS2$estimators),
data.frame(experiment = "2", comparison = "PS1 vs. PS2", PS1_PS2$estimators),
data.frame(experiment = "2", comparison = "OS1 vs. TS1", OS1_TS1$estimators),
data.frame(experiment = "2", comparison = "OS2 vs. TS2", OS2_TS2$estimators),
data.frame(experiment = "2", comparison = "OSdiff vs. TSdiff", OSdiff_TSdiff$estimators),
data.frame(experiment = "2", comparison = "PS1 vs. TS1", PS1_TS1$estimators),
data.frame(experiment = "2", comparison = "PS2 vs. TS2", PS2_TS2$estimators),
data.frame(experiment = "2", comparison = "PSdiff vs. TSdiff", PSdiff_TSdiff$estimators),
data.frame(experiment = "2", comparison = "PS1 vs. OS1", PS1_OS1$estimators),
data.frame(experiment = "2", comparison = "PS2 vs. OS2", PS2_OS2$estimators),
data.frame(experiment = "2", comparison = "PSdiff vs. OSdiff", PSdiff_OSdiff$estimators)
)
experiment2 <- experiment2 %>%
mutate(
comparison = factor(comparison),
estimator = factor(estimator))
datatable(experiment2, rownames = FALSE, filter = "top") %>%
formatRound(columns = 4:ncol(experiment2), digits = 2)Simulation #3
In this simulation there is true change in 1RM, where everyone improves, but this time variable (mean = 10, sd = 5). Let’s see how that plays out
set.seed(random.seed)
data_1RM <- tibble(
Athlete = paste0("Athlete", seq(1, n_athletes)),
TS1 = rnorm(n_athletes, 100, 10),
TS2 = TS1 + rnorm(n_athletes, 10, 5),
TSdiff = TS2 - TS1,
OS1 = biological_fixed + biological_proportional * TS1 + rnorm(n_athletes, 0, biological_random),
OS2 = biological_fixed + biological_proportional * TS2 + rnorm(n_athletes, 0, biological_random),
OSdiff = OS2 - OS1,
PS1 = measurement_fixed + measurement_proportional * OS1 + rnorm(n_athletes, 0, measurement_random),
PS2 = measurement_fixed + measurement_proportional * OS2 + rnorm(n_athletes, 0, measurement_random),
PSdiff = PS2 - PS1
)
datatable(data_1RM, rownames = FALSE, filter = "top") %>%
formatRound(columns = 2:ncol(data_1RM), digits = 2)Plotting and analysis
Repeatability
TS1_TS2 <- analyse_func(data_1RM, "TS1", "TS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -8.9189630 -10.1307971 -7.6453514
#> SD Diff 4.6115710 3.9470916 5.5538432
#> MAD 8.9578068 7.7298742 10.1662669
#> RSE 4.6312950 3.9821153 5.6201853
#> PPER 0.7142897 0.6221414 0.7848343
#> SDC 9.3118426 8.0065795 11.3001399
OS1_OS2 <- analyse_func(data_1RM, "OS1", "OS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -9.6048030 -11.3823253 -7.7025302
#> SD Diff 6.7343681 5.7274530 8.2999585
#> MAD 10.1574998 8.4501656 11.6874232
#> RSE 6.7602780 5.8218479 8.3050045
#> PPER 0.5368641 0.4501079 0.6053081
#> SDC 13.5924499 11.7056096 16.6983306
PS1_PS2 <- analyse_func(data_1RM, "PS1", "PS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -9.6707868 -11.882981 -7.4360246
#> SD Diff 7.9074379 6.782576 9.5692373
#> MAD 10.5196874 8.620761 12.3702870
#> RSE 7.9764946 6.888788 9.7321362
#> PPER 0.4662668 0.390257 0.5285653
#> SDC 16.0378172 13.850836 19.5677714
Validity (Prediction)
Observed vs True
OS1_TS1 <- analyse_func(data_1RM, "OS1", "TS1")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -0.8475765 -1.5309040 -0.1400448
#> SD Diff 2.5523202 2.2026842 3.0327781
#> MAD 2.1829967 1.7815176 2.6322982
#> RSE 2.5678697 2.2188811 3.1095988
#> PPER 0.9426184 0.8854911 0.9711095
#> SDC 5.1630480 4.4613595 6.2522674
OS2_TS2 <- analyse_func(data_1RM, "OS2", "TS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -0.1617365 -1.0211939 0.8056034
#> SD Diff 3.3630665 2.7931604 4.2245840
#> MAD 2.6118866 2.1240580 3.2592150
#> RSE 2.9964181 2.5632669 3.7849629
#> PPER 0.8983040 0.8068333 0.9429202
#> SDC 6.0247023 5.1537935 7.6101780
OSdiff_TSdiff <- analyse_func(data_1RM, "OSdiff", "TSdiff")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff 0.6858400 -0.4322269 1.8146443
#> SD Diff 4.1343727 3.5793771 4.9704161
#> MAD 3.4791955 2.9056326 4.1869027
#> RSE 2.8119809 2.4368833 3.5244330
#> PPER 0.9182789 0.8369433 0.9542845
#> SDC 5.6538666 4.8996823 7.0863475
Predicted vs True
PS1_TS1 <- analyse_func(data_1RM, "PS1", "TS1")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff -0.6662657 -1.8312715 0.4321591
#> SD Diff 4.2112919 3.6186068 5.0396329
#> MAD 3.5473282 2.9625700 4.2314086
#> RSE 4.1026745 3.5310305 4.9374405
#> PPER 0.7710925 0.6837198 0.8367766
#> SDC 8.2489800 7.0996126 9.9273895
PS2_TS2 <- analyse_func(data_1RM, "PS2", "TS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff 0.0855581 -1.196799 1.4492028
#> SD Diff 4.8396908 4.057859 5.8318617
#> MAD 3.8692842 3.141164 4.7630852
#> RSE 4.4014128 3.739475 5.4671137
#> PPER 0.7384028 0.635042 0.8125517
#> SDC 8.8496336 7.518719 10.9923689
PSdiff_TSdiff <- analyse_func(data_1RM, "PSdiff", "TSdiff")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff 0.7518238 -0.9275746 2.4979527
#> SD Diff 6.2996217 5.3560794 7.4951405
#> MAD 5.1529431 4.2207781 6.1842849
#> RSE 3.7106093 3.1525026 4.7508912
#> PPER 0.8158504 0.7021780 0.8807171
#> SDC 7.4606799 6.3385314 9.5523069
Predicted vs Observed
PS1_OS1 <- analyse_func(data_1RM, "PS1", "OS1")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff 0.1813108 -0.6796237 1.0308761
#> SD Diff 3.0902968 2.5383326 3.9167088
#> MAD 2.3630119 1.9015453 2.9935957
#> RSE 3.0158782 2.5267683 3.6938464
#> PPER 0.8961385 0.8177925 0.9463232
#> SDC 6.0638295 5.0804082 7.4269759
PS2_OS2 <- analyse_func(data_1RM, "PS2", "OS2")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff 0.2472946 -0.7795265 1.134673
#> SD Diff 3.4881795 2.9257176 4.208746
#> MAD 2.7469691 2.1998625 3.371836
#> RSE 3.4838795 2.9903921 4.302615
#> PPER 0.8422803 0.7490526 0.898956
#> SDC 7.0048091 6.0125863 8.650987
PSdiff_OSdiff <- analyse_func(data_1RM, "PSdiff", "OSdiff")
#> Bootstrap with 2000 resamples and 95% bca confidence intervals.
#>
#> estimator value lower upper
#> Mean Diff 0.06598376 -1.0052804 1.2527324
#> SD Diff 4.16947276 3.4743992 5.2334076
#> MAD 3.39029586 2.7938717 4.0918165
#> RSE 3.58770417 2.9635487 4.5261121
#> PPER 0.83015687 0.7251217 0.9019114
#> SDC 7.21356271 5.9586141 9.1003583
Save estimators in data frame:
experiment3 <- rbind(
data.frame(experiment = "3", comparison = "TS1 vs. TS2", TS1_TS2$estimators),
data.frame(experiment = "3", comparison = "OS1 vs. OS2", OS1_OS2$estimators),
data.frame(experiment = "3", comparison = "PS1 vs. PS2", PS1_PS2$estimators),
data.frame(experiment = "3", comparison = "OS1 vs. TS1", OS1_TS1$estimators),
data.frame(experiment = "3", comparison = "OS2 vs. TS2", OS2_TS2$estimators),
data.frame(experiment = "3", comparison = "OSdiff vs. TSdiff", OSdiff_TSdiff$estimators),
data.frame(experiment = "3", comparison = "PS1 vs. TS1", PS1_TS1$estimators),
data.frame(experiment = "3", comparison = "PS2 vs. TS2", PS2_TS2$estimators),
data.frame(experiment = "3", comparison = "PSdiff vs. TSdiff", PSdiff_TSdiff$estimators),
data.frame(experiment = "3", comparison = "PS1 vs. OS1", PS1_OS1$estimators),
data.frame(experiment = "3", comparison = "PS2 vs. OS2", PS2_OS2$estimators),
data.frame(experiment = "3", comparison = "PSdiff vs. OSdiff", PSdiff_OSdiff$estimators)
)
experiment3<- experiment3 %>%
mutate(
comparison = factor(comparison),
estimator = factor(estimator))
datatable(experiment3, rownames = FALSE, filter = "top") %>%
formatRound(columns = 4:ncol(experiment3), digits = 2)Combined
experiment_data <- rbind(
experiment1,
experiment2,
experiment3
)
experiment_data <- experiment_data %>%
mutate(
experiment = factor(experiment),
comparison = factor(comparison),
estimator = factor(estimator))
datatable(experiment_data, rownames = FALSE, filter = "top") %>%
formatRound(columns = 4:ncol(experiment_data), digits = 2)